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Approximation of the second fundamental form of a hypersurface of a Riemannian manifold

David Cohen-Steiner 1 Jean-Marie Morvan
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We give a general Riemannian framework to the study of approximation of curvature measures, using the theory of the normal cycle. Moreover, we introduce a differential form which allows to define a new type of curvature measure encoding the second fundamental form of a hypersurface, and to extend this notion to geometric compact subsets of a Riemannian manifold . Finally, if a geometric compact subset is close to a smooth hypersurface of a Riemannian manifold, we compare their second fundamental form (in the previous sense), and give a bound of their difference in terms of geometric invariants and the mass of the involved normal cycles.
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https://hal.inria.fr/inria-00071715
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Submitted on : Tuesday, May 23, 2006 - 6:35:38 PM
Last modification on : Friday, February 4, 2022 - 3:14:48 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:34:43 PM

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  • HAL Id : inria-00071715, version 1

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David Cohen-Steiner, Jean-Marie Morvan. Approximation of the second fundamental form of a hypersurface of a Riemannian manifold. RR-4868, INRIA. 2003. ⟨inria-00071715⟩

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